Always? Clearly not. But more recently? Absolutely. The Roger Goodell NFL, combined with the kind of community involvement now typical of NFL teams, has pushed character issues to the front burner. Violence against women has been the hot button issue, but the blowback from situations like the Josh Brent / Jerry Brown tragedy have created an extremely negative profile that the league is addressing.
And for guys like Latham, who are trying to come into the league, multiple transgressions involving substance abuse are the best way for an otherwise talented player (at the toughest position to find able players) to go undrafted. That, not some perceived lack of talent, is why he went unclaimed in the draft.